Applied Mathematics and Mechanics >
Stiffness gradient sensitivity analysis method for evaluating the vibration reduction effect of complex variable-stiffness systems
Received date: 2025-07-04
Revised date: 2025-09-02
Online published: 2025-10-29
Supported by
Project supported by the National Natural Science Foundation of China (Nos. 52241103 and 52322505) and the Natural Science Foundation of Hunan Province of China (No. 2023JJ10055)
Copyright
An analytical method is proposed with the “stiffness gradient of the response” as a sensitivity metric, and the relationships between the vibration responses and stiffness changes are established. First, a 2-degree-of-freedom (DOF) system is used as an example to propose a stiffness gradient-based evaluation method, taking the effective control bandwidth ratio as a metric of effectiveness. The results show that there is an optimal mass ratio in both variable mass and variable stiffness cases. Then, a typical 16-DOF system is used to investigate the frequency domain characteristics of the stiffness gradient values in the complex system. The distributions of stiffness gradient values show multiple peak intervals corresponding to the sensitive regions for vibration control. By assigning random mass parameters, a significant exponential decay relationship between the subsystem’s mass and effective control is identified, emphasizing the importance of the optimal mass ratio. The finite-element simulation results of solid plate models with springs and oscillators further validate the theoretical results. In short, the gradient value of stiffness effectively quantifies the effects of subsystems on vibration control, providing an analytical tool for active control in complex systems. The identified exponential decay relationship offers meaningful guidance for implementation strategies.
Xingchi CAO , Xin FANG , Dianlong YU . Stiffness gradient sensitivity analysis method for evaluating the vibration reduction effect of complex variable-stiffness systems[J]. Applied Mathematics and Mechanics, 2025 , 46(11) : 2055 -2074 . DOI: 10.1007/s10483-025-3311-6
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